Você quer dizer algo assim?
$ jq --raw-output '.values[] | [.Links,.name] | @tsv' <<< '{"values": [{"Links": "https://abc/tset", "Dates": 1540204743643, "name": "test1"}, {"Links": "https://abc/tset", "Dates": 1539256093799, "name": "test2"}]}'
https://abc/tset test1
https://abc/tset test2